29.16.1 problem 444

Internal problem ID [5042]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 444
Date solved : Tuesday, March 04, 2025 at 07:45:42 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3-x -y\right ) y^{\prime }&=1+x -3 y \end{align*}

✓ Maple. Time used: 0.552 (sec). Leaf size: 30

ode:=(3-x-y(x))*diff(y(x),x) = 1+x-3*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\left (x -1\right ) \operatorname {LambertW}\left (-2 c_{1} \left (x -2\right )\right )+2 x -4}{\operatorname {LambertW}\left (-2 c_{1} \left (x -2\right )\right )} \]

✓ Mathematica. Time used: 1.051 (sec). Leaf size: 159

ode=(3-x-y[x])D[y[x],x]==1+x-3 y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {2^{2/3} \left (x \left (-\log \left (-\frac {3\ 2^{2/3} (-y(x)+x-1)}{y(x)+x-3}\right )\right )+(x-1) \log \left (\frac {6\ 2^{2/3} (x-2)}{y(x)+x-3}\right )+\log \left (-\frac {3\ 2^{2/3} (-y(x)+x-1)}{y(x)+x-3}\right )+y(x) \left (-\log \left (\frac {6\ 2^{2/3} (x-2)}{y(x)+x-3}\right )+\log \left (-\frac {3\ 2^{2/3} (-y(x)+x-1)}{y(x)+x-3}\right )-1\right )-x+3\right )}{9 (-y(x)+x-1)}=\frac {1}{9} 2^{2/3} \log (x-2)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.200 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (-x - y(x) + 3)*Derivative(y(x), x) + 3*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x + e^{C_{1} + W\left (2 \left (x - 2\right ) e^{- C_{1}}\right )} - 1 \]